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Macaulay2Doc :: fromDual

fromDual -- ideal from inverse system

Synopsis

Description

For other examples, and a more precise definition, see inverse systems.
i1 : R = ZZ/32003[x_1..x_3];
i2 : g = random(R^1, R^{-4})

o2 = | -9407x_1^4+11805x_1^3x_2-2453x_1^2x_2^2-8097x_1x_2^3+5931x_2^4-12121x_
     ------------------------------------------------------------------------
     1^3x_3+885x_1^2x_2x_3-3884x_1x_2^2x_3+3152x_2^3x_3-5925x_1^2x_3^2+763x_
     ------------------------------------------------------------------------
     1x_2x_3^2-4763x_2^2x_3^2+1599x_1x_3^3+264x_2x_3^3+14719x_3^4 |

             1       1
o2 : Matrix R  <--- R
i3 : f = fromDual g

o3 = | x_2^2x_3-544x_1x_3^2+8256x_2x_3^2+14742x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-13876x_1x_3^2+14857x_2x_3^2-6169x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+12452x_1x_3^2-1777x_2x_3^2+7107x_3^3
     ------------------------------------------------------------------------
     x_2^3+3776x_1x_3^2-9702x_2x_3^2+9800x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-14506x_1x_3^2-5518x_2x_3^2-260x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-10861x_1x_3^2+3008x_2x_3^2+10510x_3^3
     ------------------------------------------------------------------------
     x_1^3-10158x_1x_3^2+4077x_2x_3^2+8315x_3^3 |

             1       7
o3 : Matrix R  <--- R
i4 : res ideal f

      1      7      7      1
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex
i5 : betti oo

            0 1 2 3
o5 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o5 : BettiTally

See also

Ways to use fromDual :